Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
13. Archimedes' principle If an object such as a ball is placed in a liquid, it will either sink to the bottom, float, or sink a certain distance and remain suspended in the liquid. Suppose a fluid has constant weight density w and that the fluid's surface coincides with the plane z = 4. A spherical ball remains suspended in the fluid and occupies the region x² + y² + (z – 2)² < 1. a. Show that the surface integral giving the magnitude of the total force on the ball due to the fluid's pressure is п Force = lim w(4 – za) Aok = n00 k=1 za) Δσ w(4 – z) do. b. Since the ball is not moving, it is being held up by the buoy- ant force of the liquid. Show that the magnitude of the buoy- ant force on the sphere is Buoyant force = w(z – 4)k •n doơ, where n is the outer unit normal at (x, y, z). This illustrates Archimedes' principle that the magnitude of the buoyant force on a submerged solid equals the weight of the displaced fluid. c. Use the Divergence Theorem to find the magnitude of the buoyant force in part (b).

13. Archimedes' principle If an object such as a ball is placed in a liquid, it will either sink to the bottom, float, or sink a certain distance and remain suspended in the liquid. Suppose a fluid has constant weight density w and that the fluid's surface coincides with the plane z = 4. A spherical ball remains suspended in the fluid and occupies the region x² + y² + (z – 2)² < 1. a. Show that the surface integral giving the magnitude of the total force on the ball due to the fluid's pressure is п Force = lim w(4 – za) Aok = n00 k=1 za) Δσ w(4 – z) do. b. Since the ball is not moving, it is being held up by the buoy- ant force of the liquid. Show that the magnitude of the buoy- ant force on the sphere is Buoyant force = w(z – 4)k •n doơ, where n is the outer unit normal at (x, y, z). This illustrates Archimedes' principle that the magnitude of the buoyant force on a submerged solid equals the weight of the displaced fluid. c. Use the Divergence Theorem to find the magnitude of the buoyant force in part (b).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
13. Archimedes' principle If an object such as a ball is placed in a liquid, it will either sink to the bottom, float, or sink a certain distance and remain suspended in the liquid. Suppose a fluid has constant weight density w and that the fluid's surface coincides with the plane z = 4. A spherical ball remains suspended in the fluid and occupies the region x² + y² + (z – 2)² < 1. a. Show that the surface integral giving the magnitude of the total force on the ball due to the fluid's pressure is п Force = lim w(4 – za) Aok = n00 k=1 za) Δσ w(4 – z) do. b. Since the ball is not moving, it is being held up by the buoy- ant force of the liquid. Show that the magnitude of the buoy- ant force on the sphere is Buoyant force = w(z – 4)k •n doơ, where n is the outer unit normal at (x, y, z). This illustrates Archimedes' principle that the magnitude of the buoyant force on a submerged solid equals the weight of the displaced fluid. c. Use the Divergence Theorem to find the magnitude of the buoyant force in part (b).
Transcribed Image Text:13. Archimedes' principle If an object such as a ball is placed in a liquid, it will either sink to the bottom, float, or sink a certain distance and remain suspended in the liquid. Suppose a fluid has constant weight density w and that the fluid's surface coincides with the plane z = 4. A spherical ball remains suspended in the fluid and occupies the region x² + y² + (z – 2)² < 1. a. Show that the surface integral giving the magnitude of the total force on the ball due to the fluid's pressure is п Force = lim w(4 – za) Aok = n00 k=1 za) Δσ w(4 – z) do. b. Since the ball is not moving, it is being held up by the buoy- ant force of the liquid. Show that the magnitude of the buoy- ant force on the sphere is Buoyant force = w(z – 4)k •n doơ, where n is the outer unit normal at (x, y, z). This illustrates Archimedes' principle that the magnitude of the buoyant force on a submerged solid equals the weight of the displaced fluid. c. Use the Divergence Theorem to find the magnitude of the buoyant force in part (b).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 7 steps with 7 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS